# Ideal gas law

The above diagram shows the relationship between the pressure ($$y$$-axis) and the volume ($$x$$-axis) of an ideal gas when it changes its state in the order $$A \to B \to C \to D \to A.$$ The processes $$A \to B$$ and $$C \to D$$ are isobaric processes with pressures $$2P$$ and $$P,$$ respectively. The processes $$B \to C$$ and $$D \to A$$ are isothermal processes with temperatures $$2T$$ and $$T,$$ respectively. Which of the following statements is correct?

a) The volume of the gas at state $$C$$ is $$4$$ times as large as that at state $$A.$$
b) The volume of the gas at state $$B$$ is greater than that at state $$D.$$
c) The average speed of the molecules at state $$C$$ is $$2$$ times as large as that at state $$A.$$

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